Dear all: I am currently working with a multilevel model with ITEMS (and covariate V1) nested within SUBJECT. Items were not repeated across subjects (each item looked at was novel). SUBJECTS were given a treatment (V2) in a between subject design. The dependent variable (DV) is per ITEM. I've included a dummy data set with a similar design below. I am interested in V1 and V2 as predictors, as well as the potential interaction of V1:V2. In addition, I expect varying intercepts and varying slopes for V1 within each SUBJECT. I believe this would correspond to the model: model1 <- glmer(DV ~ V1*V2 + (0 + V1|SUBJECT) + (1|SUBJECT),testdataset,family="binomial") However, I also expect V1 to have varying intercepts and slopes with respect to V2. I believe varying intercepts should be accounted for by (1|SUBJECT) because of the between subjects treatment design. Similarly, I don't believe (0 + V2|SUBJECT) would make sense, since each subject only has one value of V2. Instead, I ran a model accounting for varying slopes of the interaction V2:V1. This seemed to make sense since each V2:V1 factor should have a different slope if V1 slopes vary with respect to V2. This gives us the model: model2 <- glmer(DV ~ V1*V2 + (0 + V2:V1|SUBJECT) + (1|SUBJECT),testdataset,family="binomial") Model2 does give me different results than model1. However, because of the between subjects design for V2 treatment, I'm not clear why model2 is any different from model1. Shouldn't V2:V1 should be 0 for the non-treated value of V2 within a subject? Many thanks for help interpreting this question / design. Yours, Derek TESTDATASET: SUBJECT V2 ITEM V1 V1.nested DV S1 A 1 a A:a N S1 A 2 a A:a N S1 A 3 a A:a N S1 A 4 a A:a Y S1 A 5 a A:a Y S1 A 6 b A:b Y S1 A 7 b A:b Y S1 A 8 b A:b Y S1 A 9 b A:b Y S1 A 10 b A:b N S2 A 11 a A:a N S2 A 12 a A:a N S2 A 13 a A:a Y S2 A 14 a A:a Y S2 A 15 a A:a Y S2 A 16 b A:b Y S2 A 17 b A:b Y S2 A 18 b A:b Y S2 A 19 b A:b N S2 A 20 b A:b Y S3 A 21 a A:a N S3 A 22 a A:a Y S3 A 23 a A:a N S3 A 24 a A:a N S3 A 25 a A:a N S3 A 26 b A:b Y S3 A 27 b A:b Y S3 A 28 b A:b Y S3 A 29 b A:b Y S3 A 30 b A:b Y S4 A 31 a A:a N S4 A 32 a A:a N S4 A 33 a A:a N S4 A 34 a A:a N S4 A 35 a A:a N S4 A 36 b A:b Y S4 A 37 b A:b Y S4 A 38 b A:b N S4 A 39 b A:b Y S4 A 40 b A:b N S5 B 41 a B:a N S5 B 42 a B:a N S5 B 43 a B:a Y S5 B 44 a B:a N S5 B 45 a B:a Y S5 B 46 b B:b Y S5 B 47 b B:b Y S5 B 48 b B:b N S5 B 49 b B:b Y S5 B 50 b B:b N S6 B 51 a B:a N S6 B 52 a B:a Y S6 B 53 a B:a Y S6 B 54 a B:a N S6 B 55 a B:a N S6 B 56 b B:b Y S6 B 57 b B:b Y S6 B 58 b B:b N S6 B 59 b B:b N S6 B 60 b B:b Y S7 B 61 a B:a N S7 B 62 a B:a N S7 B 63 a B:a Y S7 B 64 a B:a N S7 B 65 a B:a N S7 B 66 b B:b N S7 B 67 b B:b Y S7 B 68 b B:b Y S7 B 69 b B:b Y S7 B 70 b B:b N S8 B 71 a B:a N S8 B 72 a B:a N S8 B 73 a B:a N S8 B 74 a B:a N S8 B 75 a B:a Y S8 B 76 b B:b Y S8 B 77 b B:b Y S8 B 78 b B:b N S8 B 79 b B:b Y S8 B 80 b B:b N S9 B 81 a B:a Y S9 B 82 a B:a N S9 B 83 a B:a N S9 B 84 a B:a N S9 B 85 a B:a N S9 B 86 b B:b N S9 B 87 b B:b N S9 B 88 b B:b N S9 B 89 b B:b Y S9 B 90 b B:b Y -- Derek Dunfield, PhD Postdoctoral Fellow, MIT Intelligence Initiative Sloan School of Management MIT Center for Neuroeconomics, Prelec Lab 77 Massachusetts Ave E62-585 Cambridge MA 02139
Varying slopes in a multilevel model with a between subjects treatment
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